Equilibrium of Heterogeneous Congestion Control: Optimality and Stability

When heterogeneous congestion control protocols that react to different pricing signals share the same network, the current theory based on utility maximization fails to predict the network behavior. The pricing signals can be different types of signals such as packet loss, queueing delay, etc, or different values of the same type of signal such as different ECN marking values based on the same actual link congestion level. Unlike in a homogeneous network, the bandwidth allocation now depends on router parameters and flow arrival patterns. It can be non-unique, suboptimal and unstable. In Tang et al. (“Equilibrium of heterogeneous congestion control: Existence and uniqueness,” IEEE/ACM Trans. Netw., vol. 15, no. 4, pp. 824–837, Aug. 2007), existence and uniqueness of equilibrium of heterogeneous protocols are investigated. This paper extends the study with two objectives: analyzing the optimality and stability of such networks and designing control schemes to improve those properties. First, we demonstrate the intricate behavior of a heterogeneous network through simulations and present a framework to help understand its equilibrium properties. Second, we propose a simple source-based algorithm to decouple bandwidth allocation from router parameters and flow arrival patterns by only updating a linear parameter in the sources’ algorithms on a slow timescale. It steers a network to the unique optimal equilibrium. The scheme can be deployed incrementally as the existing protocol needs no change and only new protocols need to adopt the slow timescale adaptation

Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs

Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for high-dimensional problems. One fundamental numerical difficulty is that random samples in the training set introduce statistical errors into the discretization of loss functional which may become the dominant error in the final approximation, and therefore overshadow the modeling capability of the neural network. In this work, we propose a new minmax formulation to optimize simultaneously the approximate solution, given by a neural network model, and the random samples in the training set, provided by a deep generative model. The key idea is to use a deep generative model to adjust random samples in the training set such that the residual induced by the approximate PDE solution can maintain a smooth profile when it is being minimized. Such an idea is achieved by implicitly embedding the Wasserstein distance between the residual-induced distribution and the uniform distribution into the loss, which is then minimized together with the residual. A nearly uniform residual profile means that its variance is small for any normalized weight function such that the Monte Carlo approximation error of the loss functional is reduced significantly for a certain sample size. The adversarial adaptive sampling (AAS) approach proposed in this work is the first attempt to formulate two essential components, minimizing the residual and seeking the optimal training set, into one minmax objective functional for the neural network approximation of PDEs

Using canopy greenness index to identify leaf ecophysiological traits during the foliar senescence in an oak forest

© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Ecosphere 9 (2018): e02337, doi:10.1002/ecs2.2337.Camera‐based observation of forest canopies allows for low‐cost, continuous, high temporal‐spatial resolutions of plant phenology and seasonality of functional traits. In this study, we extracted canopy color index (green chromatic coordinate, Gcc) from the time‐series canopy images provided by a digital camera in a deciduous forest in Massachusetts, USA. We also measured leaf‐level photosynthetic activities and leaf area index (LAI) development in the field during the growing season, and corresponding leaf chlorophyll concentrations in the laboratory. We used the Bayesian change point (BCP) approach to analyze Gcc. Our results showed that (1) the date of starting decline of LAI (DOY 263), defined as the start of senescence, could be mathematically identified from the autumn Gcc pattern by analyzing change points of the Gcc curve, and Gcc is highly correlated with LAI after the first change point when LAI was decreasing (R2 = 0.88, LAI < 2.5 m2/m2); (2) the second change point of Gcc (DOY 289) started a more rapid decline of Gcc when chlorophyll concentration and photosynthesis rates were relatively low (13.4 ± 10.0% and 23.7 ± 13.4% of their maximum values, respectively) and continuously reducing; and (3) the third change point of Gcc (DOY 295) marked the end of growing season, defined by the termination of photosynthetic activities, two weeks earlier than the end of Gcc curve decline. Our results suggested that with the change point analysis, camera‐based phenology observation can effectively quantify the dynamic pattern of the start of senescence (with declining LAI) and the end of senescence (when photosynthetic activities terminated) in the deciduous forest.Priority Academic Program Development of Jiangsu Higher Education Institutions in Discipline of Environmental Science and Engineer in Nanjing Forest University; China Scholarship Council Grant Number: 201506190095; Brown University Seed Funds for International Research Projects on the Environmen